1. Field of the Invention
This invention relates generally to suspension systems and methods for isolating or reducing the transmission of vibratory motion between an object and a base and, more particularly, to a damped vibration isolation or suspension system that exhibits low stiffness to effectively reduce the transmission of omnidirectional vibratory motion and further includes improved damping to effectively limited resonant responses of the system to values as low as or lower than those of critically damped, viscously damped systems while still providing effective isolation at higher frequencies. In some forms and applications of the present invention, the system provides isolation, rather than amplification over a wide range of frequencies which include the resonant frequencies of the system. The present invention is also directed to the method of adding damping to a particular isolation system which relies on elastic structures loaded to approach their so-called point of elastic instability to create an overall system which can minimize resonant responses while still providing effective isolation at higher frequencies.
2. Description of Related Art
The problems caused by unwanted vibration on motion-sensitive equipment and devices have been widely researched and numerous solutions to prevent or reduce the transmission of vibratory motion have been proposed and developed. Many of the devices designed to reduce the transmission of unwanted vibration between an object and its surroundings, commonly called vibration isolators or suspension devices, have utilized various combinations of elements such as resilient pads made from a variety of materials, various types of mechanical springs, and pneumatic devices which help reduce the effects of vibration found near the object to be isolated. There are, however, serious shortcomings and disadvantages associated with these particular prior art isolation systems which prevent them from obtaining low system natural frequencies while providing high isolation performance at low as well as high frequencies.
These shortcomings and disadvantages were addressed through my development of a novel vibration isolation system described in my co-pending application Ser. No. 395,093, filed Aug. 16, 1989, entitled "VIBRATION ISOLATION SYSTEM" which is hereby incorporated by reference in this present application. The particular vibration isolation system described in my co-pending application and utilized in connection with the present invention provides versatile vibration isolation by exhibiting low stiffness in an axial direction (generally the direction of the payload weight) and any direction substantially transverse to the axial direction. The particular system utilizes a combination of isolators that can be connected together in series to provide omnidirectional isolation. Each isolator is designed to isolate either the axial or the transverse component of any vibratory motion to effectively isolate vibrations in all directions.
Each isolator relies on a principle of loading a particular elastic structure which forms the isolator or a portion of it (the loading being applied by either the weight of the object, the combined weight of the object and another isolator, or by an external loading mechanism) to approach the elastic structure's point of elastic instability. This point of elastic instability, also called the "critical buckling load" of the structure causes a substantial reduction of either the axial or transverse stiffness of the isolator to create zero or near zero stiffness in the axial and any transverse direction. The isolators still retain sufficient axial stiffness to support the payload weight; however, there will be little or no stiffness in both the axial or transverse directions. As a result, the isolators suppress the transmission of vibratory motion between an object and a base. The magnitude of the stiffness of each particular isolator depends upon how closely the point of instability is approached.
If the load on the isolator's elastic structure is greater than the critical buckling load, the excessive load will tend to propel the structure into its buckled shape, creating a "negative-stiffness" or "negative-spring-rate" mechanism. By combining a negative-stiffness mechanism with a positive spring, adjusted so that the positive stiffness of the isolator cancels or nearly cancels the negative stiffness, the resulting device can be placed at or near its point of elastic instability. The magnitude of the load causing the negative stiffness can be adjusted, creating an isolator that can be "fine tuned" to the particular stiffness desired. In subsequent discussions, this means for reducing the stiffness of the elastic structure of the isolator will be referred to as a stiffness-reducing mechanism or negative-stiffness mechanism.
One of the properties associated with my vibration isolation system is the system's ability to significantly increase the inherent damping within the structure (e.g., the support springs, the radial flexures and the column members) through the compressive loading of these structures to approach their point of elastic instability. This principle, referred to herein as the damping multiplication effect, occurs when stiffness is reduced within the structure by the negative-stiffness mechanism. This damping multiplication effect can transform a lightly damped structure into a highly damped structure simply by applying a sufficient amount of loading force to the elastic structure. While the structure and method for creating this damping multiplication effect were fully disclosed in my co-pending application, the damping multiplication effect was not fully recognized, and a full explanation of this effect will now be provided. First, a brief discussion of the effects of damping will be provided.
Damping in prior art vibration isolation systems is frequently described in terms of critical damping ratio or percent critical damping, which refers to systems with viscous damping, although the damping mechanism may not actually be viscous damping. Damping in the preferred embodiments of my isolation system more closely approximates hysteretic damping or structural damping and is described in terms of "loss factor". Hysteretic damping is generally superior to viscous damping in vibration isolation systems, particular those with high damping, because hysteretic damping can limited the isolation system resonant responses to low values and still provide low transmissibility at higher frequencies. High damping in viscously damped systems seriously degrades the isolation system performance at higher frequencies. FIG. 12 shows the effects of damping on the transmissibility versus frequency ratio for a hysteretically damped system. Also, for comparison, a transmissibility versus frequency ratio curve is shown in a dashed line in FIG. 12 for a viscously damped system that has the same resonant response as the hysteretically damped system with a loss factor of 1.0 (the viscous critical damping ratio is 0.5). A loss factor of 2.0 corresponds to critical damping (i.e., a critical damping ratio of 1.0 for a viscously damped system). The transmissibility at resonance for this case is approximately 1.12. Resonant responses this low and lower can be achieved with the present isolation system, as well as hysteretic-damping-type transmissibility versus frequency ratio behavior closely approximating that of FIG. 12.
The damping multiplication effect inherent in my vibration isolation system can be explained by the following principles. First, consider an isolation system as shown in FIGS. 1 and 2 herein in which the elastic structure connected between the object and the base has an initial stiffness K.sub.s and an initial loss factor .eta..sub.s prior to application of the stiffness-reducing mechanism. The loss factor can be expressed in terms of the ratio of the energy dissipated per cycle to the maximum elastic energy stored during the cycle, i.e.: ##EQU1## Also, since: EQU (maximum energy stored during cycle)=1/2K.sub.s .delta..sup.2 ( 2)
where .delta. is the amplitude of the system displacement, ##EQU2## The loss factor .eta. for the system with reduced stiffness K has the same form as Eqs. 1 and 3, i.e., ##EQU3## As the net stiffness of the system is reduced by the stiffness-reducing mechanism, the maximum elastic energy stored in the system during the cycle, 1/2K.delta..sup.2 is reduced, but the energy dissipated in the system per cycle is not reduced. This energy dissipated is, according to Eq. 3, EQU (energy dissipated per cycle)=.pi..eta..sub.s K.sub.s .delta..sup.2 ( 5)
With Eqs. 4 and 5, the loss factor for the reduced-stiffness system is: ##EQU4## Thus, the loss factor for the reduced stiffness system is equal to the initial loss factor for the unloaded elastic structure, multiplied by the ratio of the initial stiffness to the reduced stiffness. Since, with the stiffness-reducing mechanism, the system stiffness can be reduced significantly, large values of the damping multiplication factor K.sub.s /K can be achieved.
Damping inherent in a structure, typically referred to as structural damping, includes hysteretic damping in the structural material and, if the structure is a built-up structure such as two or more sections bolted together, joint friction or interface damping as well.
The damping multiplication effect can significantly increase the damping in an elastic structure, such as a high strength steel structure, which has a loss factor typically below 0.01 when unloaded. The damping can be increased a hundred fold and greater through the application of the compression forces that load the structure towards its point of elastic instability to produce a loss factor exceeding 1.0. Substantially higher damping can be produced if the elastic structure being loaded to approach its point of elastic instability has higher damping to begin with, such as a rubber spring.
Many of the applications of my vibration isolation system have input vibrations over a range of frequencies that include the resonant frequencies of the system. Often there is a need to limit the response of the payload at the resonant frequencies of the system and to even minimize the response while still providing effective isolation at higher frequencies. In some applications, the multiplication effect can sufficiently increase the damping inherent in my isolation system structure so that no further damping of the system is required. In other applications, additional damping is desirable.
Therefore, it is desirable to add damping to my vibration isolation system for applications requiring high damping in order to significantly limit or minimize the system's resonant responses. However, isolation at higher frequencies should not be significantly compromised when adding damping to my vibration isolation system. Further, the use of added damping should not degrade the system (or should degrade it as little as possible) regarding its other benefits such as resistance to adverse environments, limited performance variations with fluctuating temperatures and dimensional stability.